The numbers lead a dance Mathematics of the Sestina

Alan R. Champneys, Poul G. Hjorth, Harry Man

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Abstract

Sestinas are poems of 39 lines comprising six verses of six lines each, and a three line final verse or 'envoi'. The structure of the sestina is built around word repetition rather than strict rhyme. Each verse uses the same set line ending words, but in a permuted order. The form of the permutation is highly specific, and is equivalent to iteration of the tent map. This paper considers for which number N of verses, other than 6, can a sestina-like poem be formed. That is, which N will the prescribed permutation lead to a poem of N verses where no two verses have the same order of their end words. In so doing, a link is found between permutation groups, chaotic dynamics, and Cunningham numbers.
Original languageEnglish
Title of host publicationNon-linear partial differential equations, mathematical physics, and stochastic analysis: the Helge Holden anniversary volume
PublisherEuropean Mathematical Society Publishing House
Publication date2018
Pages55-71
ISBN (Print)9783037191866
DOIs
Publication statusPublished - 2018
EventNon-linear PDEs, Mathematical Physics and Stochastic Analysis - Norwegian University of Science and Technology, Trondheim, Norway
Duration: 4 Jul 20167 Jul 2016

Conference

ConferenceNon-linear PDEs, Mathematical Physics and Stochastic Analysis
LocationNorwegian University of Science and Technology
CountryNorway
CityTrondheim
Period04/07/201607/07/2016
SeriesEMS Series of Congress Reports
ISSN2523-515X

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